Slow 'show tables' queries on multi-site install

Hello:

I was wondering if anyone has come across this issue with larger multi-site installs. I admin a network of about 3500 sites with the same number of users. As our network grew, I began to notice that our main blog (site ID 1) was very slow to load (8-12 seconds) most pages. From what I can tell from the MySQL slow query log, it seems to be 'show tables' queries causing the slow down. We have around 31,000 tables in the DB.

We are running MySQL 5.1.50 Clustered. The cluster is quite robust, so its surprising to see this behaviour. Slow load times do not occur on any other network sites. I have disabled all plug-ins to test that theory, with no improvement. The P3 Performance analysis plugin also reports very fast load times related to any plug-ins we are running when they are enabled. The slow response portion is simply referred to as "WordPress Core".

Thanks for any insight.